Open Access
April 2019 Rank verification for exponential families
Kenneth Hung, William Fithian
Ann. Statist. 47(2): 758-782 (April 2019). DOI: 10.1214/17-AOS1634

Abstract

Many statistical experiments involve comparing multiple population groups. For example, a public opinion poll may ask which of several political candidates commands the most support; a social scientific survey may report the most common of several responses to a question; or, a clinical trial may compare binary patient outcomes under several treatment conditions to determine the most effective treatment. Having observed the “winner” (largest observed response) in a noisy experiment, it is natural to ask whether that candidate, survey response or treatment is actually the “best” (stochastically largest response). This article concerns the problem of rank verification—post hoc significance tests of whether the orderings discovered in the data reflect the population ranks. For exponential family models, we show under mild conditions that an unadjusted two-tailed pairwise test comparing the first two-order statistics (i.e., comparing the “winner” to the “runner-up”) is a valid test of whether the winner is truly the best. We extend our analysis to provide equally simple procedures to obtain lower confidence bounds on the gap between the winning population and the others, and to verify ranks beyond the first.

Citation

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Kenneth Hung. William Fithian. "Rank verification for exponential families." Ann. Statist. 47 (2) 758 - 782, April 2019. https://doi.org/10.1214/17-AOS1634

Information

Received: 1 February 2017; Revised: 1 June 2017; Published: April 2019
First available in Project Euclid: 11 January 2019

zbMATH: 07033150
MathSciNet: MR3909949
Digital Object Identifier: 10.1214/17-AOS1634

Subjects:
Primary: 62F07
Secondary: 62F03

Keywords: exponential family , multiple comparison , ranking , sample best , selective inference

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.47 • No. 2 • April 2019
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